1. Technical Field
The present invention relates to a position calculating method and a position calculating device.
2. Related Art
A GPS (Global Positioning System) is widely known as a positioning system using a positioning signal, and is used for a position calculating device built into a mobile phone, a car navigation apparatus, or the like. The GPS performs a position calculation operation for calculating a timepiece error and the position coordinates of a position calculating device on the basis of information, such as the positions of a plurality of GPS satellites or a pseudorange from each GPS satellite to the position calculating device.
As the position calculation operation using a satellite positioning system, a position calculation operation using a so-called least square method of minimizing the sum of the squares of the errors (hereinafter, referred to as “an error of the pseudorange”), which may be included in the pseudorange, using the pseudoranges calculated for a plurality of satellites is known (for example, refer to JP-A-2009-97897).
In general, the position calculation operation using the least square method is an effective technique when approximately calculating a timepiece error and the position coordinates of a position calculating device when the number of positioning satellites, which have been successfully captured, is larger than the number of unknowns (in an overdetermined state). However, the position calculated using the least square method is not necessarily reliable.
If an error of the pseudorange can definitely be regarded as white noise at all times, the position calculated using the least square method may be reliable. Mathematically speaking, this is a case where the distribution of error of the pseudorange follows normal distribution (Gaussian distribution). However, this is just an ideal case.
In a satellite positioning system, various errors may be included in the measured pseudorange due to various error factors. A typical example thereof is a multi-path. In a so-called multi-path environment, a satellite signal reaches a position calculating device through two or more paths. A signal that the position calculating device receives is a signal (multi-path signal) in which indirect wave signals, such as a reflected wave reflected from buildings or the ground, a transmitted wave transmitted through an obstacle, and a diffracted wave diffracted by an obstacle, are superimposed on a direct wave signal which is a satellite signal transmitted from a positioning satellite. The indirect wave signal reaches the position calculating device with a path length which is larger than that of the direct wave signal. Due to the influence of the indirect wave signal, an undetermined error which does not follow the normal distribution may be included in the pseudorange measured by the position calculating device.